SOLUTION: Five brothers, A,B,C,D and E, bought a car for $42000. A paid one third of the sum of the amounts paid by the other brothers. B paid one quarter of the sum of the amounts paid by t

Question 1104665: Five brothers, A,B,C,D and E, bought a car for $42000. A paid one third of the sum of the amounts paid by the other brothers. B paid one quarter of the sum of the amounts paid by the other brothers. C paid one fifth ot the sum of the amounts paid by the other brothers. D paid one sixth of the sum of the amounts paid by the other brothers. How much did E pay?
Answer by ikleyn(52921) (Show Source): You can put this solution on YOUR website!
.

Let a = amount paid by A
    b =             by B
    c =             by C
    d =             by D
    e =             by E.


Then

a =         (1)
b =         (2)
c =         (3)
d =         (4)


Multiply equations: (1) by 3;  (2) by 4; (3) by 5;  and (4) by 6.  The modified system is

3a = b + c + d + e       (5)
4b = a + c + d + e       (6)
5c = a + b + d + e       (7)
6d = a + b + c + e       (8)


Add "a" to both sides of (5).  Add "b" to both sides of (6).  Add "c" to both sides of (7),  Add "d" to both sides of (8).


Use the fact that a + b + c + d + e = 42000.   You will get

4a = 42000  ====>  a =  = 10500.     (9)
5b = 42000  ====>  b =  =  8400.    (10)
6c = 42000  ====>  c =  =  7000.    (11)
7d = 42000  ====>  d =  =  6000.    (12)

Then  a + b + c + d = 10500 + 8400 + 7000 + 6000 = 31900,

and   e = 42000 - 31900 = 10100.


Answer.  E payed 10100.

Solved.

RELATED QUESTIONS
Four friends bought a boat for $1200. Friend A paid half the sum of the amounts paid by... (answered by josgarithmetic,ikleyn,MathTherapy)

A car bought for Rs 1,000,000 depreciates each year by 5% what is the insurance premium... (answered by Alan3354,ikleyn)

How to write an algebraic model and solve the problem. You and your two sisters... (answered by Theo)

David has two brothers. One brother is two years younger than him and the other is five... (answered by ewatrrr)

During a half- price sale Mr. Kamaran bought a notebook for the usual price and a second... (answered by richwmiller)

The sum of two brothers is 46. The younger brother is 10 more than a third of the older... (answered by 1335)

A college student bought 11 books for fall classes. If the cost of his anatomy textbook... (answered by ewatrrr)

The graph illustrates a normal distribution for the prices paid for a particular model of (answered by Boreal)

The sum of the ages of four brothers in a family is 31. If the oldest brother is 6 years... (answered by josgarithmetic)